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Example of a Bayesian Network: Faulty Fan
Consider an office scenario where an electric fan fails to spin. The possible causes include a faulty fan (with a failure probability of 0.02) or a faulty extension plug (with a failure probability of 0.2). If a mobile phone charger connected to the same plug works well, what is the probability that the problem is caused by a faulty fan? This scenario can be represented as a simple Bayesian network, shown below. The nodes "Faulty Fan" and "Faulty Plug" are parents of the random variable "Fan", whereas the child of "Fan" is "No Spin". The variables "Faulty Fan" and "Faulty Plug" are marginally independent but become conditionally dependent given "Fan". Due to these dependencies and conditional probabilities, a Bayesian network corresponds to a directed acyclic graph where no loops or self-connections are allowed.

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